# A decomposition technique in integer linear programming

Computational Techniques

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## Abstract

In this work, using the group theoretical approach we point out so me conditions on the B^{−1}N matrix, often verified in practice, that make it possible to transform the system of linear congruences (constraints of problem 2) in a block diagonal form. In some cases, using this proce dure, the number of constraints can increase with respect to the number of constraints of problem 2. However, the problem can be solved indipen dently for the variables associated with each block.

This procedure leads to the indipendent solution of a number of subproblems in a smaller number of variables.

In the worst case each subproblem requires the same number of constraints as the original problem, but generally this number is smaller.

## Keywords

Integer Programming Integer Linear Programming Linear Programming Problem Mixed Integer Linear Programming Decomposition Technique
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## Copyright information

© Springer-Verlag Berlin Heidelberg 1976